   Chapter 11.1, Problem 46E

Chapter
Section
Textbook Problem

Determine whether sequence converges or diverges. If it converges, find the limit.46. an = 2−ncos nπ

To determine

Whether the sequence converges or diverges and obtain the limit if the sequence converges.

Explanation

Given:

The sequence is an=2ncosnπ (or) an=cosnπ2n .

Definition used:

If an is a sequence and limnan exists, then the sequence an is said to be converges; otherwise it diverges.

Theorem used: Squeeze Theorem:

If xnznyn for nN and limnxn=limnyn=L then the value of limnzn is L.

Calculation:

Obtain the limit of the sequence to investigate whether the sequence converges or diverges.

Compute the value of limnan=limncosnπ2n .

Since 1cosnπ1 and divide by 2n , apply the Squeeze Theorem and obtain the relation as follows:

12ncosnπ2n12n

limn(12n)limn(cosnπ2n)limn(12n) (1)

Obtain the value of limn(12n)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find dy/dx by implicit differentiation. 7. x4 + x2y2 + y3 = 5

Single Variable Calculus: Early Transcendentals, Volume I

In Problems 1-4, express each inequality as a constraint. 3.

Mathematical Applications for the Management, Life, and Social Sciences

Sometimes, Always, or Never: dx equals the area between y = f(x), the x-axis, x = a, and x = b.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 